Image providing method and device

ABSTRACT

Visual-field information including information on sight-line direction (theta, phi) and on field angle (gamma) in visual-field area of input fish-eye image is input in real-time. From the input visual-field information, a drawing area of a plane is calculated in real-time that is orthogonal to the sight-line direction and has an extent determined by the field angle. A pixel position in the fish-eye image that corresponds to each pixel position in the calculated drawing area is determined. This forms in real-time a dewarped image from the fish-eye image with its distortion removed.

CROSS-REFERENCE TO PRIOR APPLICATION

This application is based upon and claims the benefit of priority fromthe prior Japanese Patent Application No. 2004-158855, filed on May 28,2004, the entire content of which is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an image providing method and devicewhich nonlinearly develops on a display plane an image in any sight-linedirection in a fish-eye image (omnidirectional image), and moreparticularly, to an interactive type image providing method and devicewhich can provide in real-time an moving image in a direction intendedby an observer.

2. Description of the Related Art

In a monitoring system using a monitoring camera, for example, a methodis known for collecting a wide-angle image using a monitoring camerawith a fish-eye lens instead of a monitoring camera with a usual lens toobtain a wider monitorable area. In this case, a monitoring camera witha fish-eye lens provides an fish-eye image more distorted than an imageprovided by a monitoring camera with a usual lens. A non-lineartransformation processing is thus known that displays on a plane adistortion-removed image in any sight-line direction from the fish-eyeimage. Such a non-linear transformation processing is referred to anormalization processing (dewarp).

Known methods for dewarping a fish-eye image include, for example,methods disclosed in Japanese patents No. 3051173 and No. 3126955.Dewarping logics are formulated into transformation equations that aregenerally similar. The dewarping methods have thus been implemented as adevice with a programming language using any transformation equation, orimplemented after fixing areas to be drawn at a plurality of places andcreating previously a transformation rule in a table-lookup form basedon a equation.

In the method disclosed in Japanese patent No. 3051173 on page 5 in theright column for lines 19 through 30 and FIG. 4, X-MAP processor andY-MAP processor speed up the mapping on a sphere. Also in the methoddisclosed in Japanese patent No. 3126955 on page 5, paragraph 0021, andFIG. 1, two coordinate-operation parts use a look-up table to speed upthe coordinate computation on a sphere.

In both methods disclosed in above-mentioned Japanese patents No.3051173 and No. 3126955, however, a non-linear transformation processinguses a mapping on a sphere as a basis to sequentially calculate displaypixels, and the dewarping is only performed in visual fields from aplurality of predetermined limited places, thereby providing poorinteractivity.

SUMMARY OF THE INVENTION

An image providing device according to an aspect of the presentinvention comprises: a fish-eye image input device inputting fish-eyeimage; a fish-eye image storage device storing said input fish-eyeimage; a visual-field information input device inputting in real-timevisual-field information including information on sight-line direction(theta, phi) and on field angle (gamma) in visual-field area of saidfish-eye image; a drawing area calculation device for calculating inreal-time, using said input visual-field information, each pixel of adrawing area in a plane which is orthogonal to said sight-line directionand has an extent determined by said field angle; and a dewarpingprocessing device determining a pixel position in said fish-eye imagewhich corresponds to each pixel position in said calculated drawing areato form in real-time a dewarped image from the fish-eye image with itsdistortion removed.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates basic concept of the dewarping processing accordingto the present invention.

FIG. 2 illustrates basic concept of the dewarping processing accordingto the present invention.

FIG. 3 illustrates basic concept of the dewarping processing accordingto the present invention.

FIG. 4 shows a configuration of an interactive type image display systemaccording to the first embodiment of the present invention.

FIG. 5 is a flowchart of the operation of an image-providing device inthe display system in FIG. 4.

FIG. 6 shows the operation of a dewarping-computing module in theimage-providing device in FIG. 5.

FIG. 7 is a flowchart of the operation of the dewarping-computing modulein FIG. 6.

FIG. 8 shows a processing of an image-providing device according to thesecond embodiment of the present invention.

FIG. 9 shows a fish-eye image divided into a plurality of blocks that ishandled in an image-providing device according to the third embodimentof the present invention.

FIG. 10 shows a stereo image display system according to the fourthembodiment of the present invention.

FIG. 11 illustrates the operation of the system in FIG. 10.

FIG. 12 illustrates the operation of the system in FIG. 10.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, embodiments of the present invention willbe described below.

Basic Concept of the Dewarping Processing

FIGS. 1 to 3 illustrate the basic concept of the dewarping processingaccording to the embodiment of the present invention.

As shown in FIG. 1, a fish-eye image can be regarded as an image(distorted all-direction image) derived from an object imaged on ahemispherical surface of a virtually established hemisphere S beingdeveloped on a plane (the circular bottom surface of the hemisphere S).In this hemisphere S, with the origin O being at the center of itsbottom circle, a three-dimensional coordinate system is established withorthogonal directions X-axis and Y-axis from the origin O in a planeincluding the bottom circle and the direction Z-axis from the origin Oextending toward the vertex of the hemisphere S.

Input information is now given as sight-line direction B from the originO toward the hemispherical surface. Sight-line direction B is given by azenithal angle (tilt) theta of an angle from Z-axis and an azimuthalangle (pan) phi of an angle from X-axis. This sight-line direction B isa visual-field center of a viewer. As shown in FIG. 2, an additionallyspecified zoom magnification (field angle gamma) specifies a portion tobe drawn (viewed) as plane A (imaging plane of a virtual perspectivecamera) that is orthogonal to sight-line direction B and tangent to thehemispherical surface shown in FIG. 1. Any position in plane A can beexpressed in a two-dimensional coordinate system of Eu and Ev with theorigin at intersection P with a line indicating sight-line direction B.This plane A is referred to a ″ drawing area. “Dewarping processing”corresponds to reconstruction of this drawing area from the originalfish-eye image (distorted all-direction image developed on the circularbottom surface of hemisphere S).

A description will now be given of the processing of reconstruction ofthe drawing area from the fish-eye image. For example, point Ps on planeA is expressed as an intersection between plane A and light ray C thatis defined by zenithal angle theta s and azimuthal angle phi s. Thebrightness of point Ps can thus be determined by calculating thethree-dimensional coordinates of point Ps with theta and phi ofsight-line direction B to determine theta s and phi s of light ray Cpassing through point Ps, and by determining the pixel position ofcorresponding point Ps′ in the fish-eye image based on a model equationof the fish-eye projection.

Specifically, given that hemisphere S is a unit sphere of radius=1 andplane A indicating the drawing area has a length of 2 Ku in Eu-axisdirection and a length of 2 Kv in Ev-axis direction as shown in FIG. 2,Ku and Kv can be determined with a zoom magnification (field anglegamma) and the aspect ratio alpha of drawing area, as follows.Ku=tan(gamma/2)Kv=alpha*tan(gamma/2)   (Equation 1)

The aspect ratio alpha depends on the window size of the drawing area.Given that the position in Eu-axis direction in plane A is u and theposition in Ev-axis direction in plane A is v, three-dimensionalcoordinates (Px, Py, Pz) of point Ps can be determined as follows.Px=−u*Ku*sin phi−v*Kv*cos phi*cos theta+sin theta*cos phiPy=u*Ku*cos phi−v*Kv*sin phi*cos theta+sin theta*sin phiPz=v*Kv*sin theta+cos theta   (Equation 2)The zenithal angle theta s and azimuthal angle phi s of point Ps canthus be determined with Px, Py, and Pz determined, as follows.theta s=tan⁻¹( (Px ² +Py ²)^(1/2) /Pz))phi s=tan⁻¹(Py/Px)   (Equation 3)

The theta s and phi s determined can provide polar coordinates (L, phis) of point Ps′ in fish-eye image G corresponding to point Ps in planeA. As shown in FIG. 3, L is commonly expressed as a one-valued functionof L=f (theta), and L=f*theta s is used as a model equation forequidistant projection and L=2f*tan (theta/2) for equi-solid-angleprojection. The f is a focal length of the fish-eye lens.

With fish-eye image G having a radius of r_px, and with the use of modelequation in the following Equation 4 in which point Ps′ is equidistantlyprojected from the center position O of fish-eye image G to theoutermost periphery of fish-eye image G when zenithal angle theta svaries from 0 to pi/2, L can be determined as follows.L=2*r _(—) px*theta s/pi   (Equation 4)The position in the X-Y coordinate system of point Ps′ in fish-eye imageG corresponding to point Ps in plane A can thus be determined by thefollowing Equation 5.X_pixel=L*cos(phi s)Y_pixel=L*sin(phi s)   (Equation 5)

In each of above-described equations, the focal position of the fish-eyelens and the resolution of the imaging element and the like may changethe radius r_px of fish-eye image G and the pixel correspondence betweenthe fish-eye image and dewarped image. Therefore, lens characteristicsand CMOS (or CCD) characteristics are preferably considered in Ku and Kvcalculation and dewarping processing.

These image transformation computations generally take a long time andmake it difficult to realize the real-time processing. To allow for suchan image transformation computation at higher speed, it is preferredthat the management function device for general management including theinput and output of images to and from the external and the interfacewith input device is separated from the computing module function fordewarping distortion. The dewarping-computing module preferably usesthree parallel-processable computing modules.

The First Embodiment

FIG. 4 shows a configuration of an interactive type image display systemaccording to the first embodiment of the present invention. This systemincludes: image providing device 1 for transforming a fish-eye image toa dewarped image in a designated visual-field; fish-eye imaging device 2for providing in real-time an all-direction image, particularly a movingimage, to the image providing device 1; digital-image file storage unit3 for accumulating a fish-eye image that is previously imaged by thefish-eye imaging device and the like in a form of a digital-image filesuch as MPEG 2 file and JPEG file group and the like; input device 4 forinputting, as an external control, information such as the user-desiredsight-line direction (theta, phi) and zoom magnification (field anglegamma); and output device 5 such as a monitor for displaying thedewarped image dewarped by image providing device 1.

Image providing device 1 includes mainly input processing unit 11 forperforming an input processing (such as A/D conversion and variousdecoding processings) of the fish-eye image; transformation device 12which is the core part of device 1; and D/A conversion unit 13 as anoutput part. Image providing device 1 also includes: input interface 14for inputting information, such as a sight-line direction, from inputdevice 4; fish-eye image storage unit 16 for storing original fish-eyeimage; and dewarped-image storage unit 18 for storing dewarped image.

Transformation device 12 further includes, management function unit 21for overall management including the input and output of fish-eye imageand dewarped image to and from the external and the interface with inputdevice 4, and dewarping computing module 22 for dewarping distortion offish-eye image.

The above-described configuration incorporates the image that is imagedby fish-eye imaging device 2 to the internal in real-time via inputprocessing unit 11 and holds the image in fish-eye image storage unit 16as an fish-eye image, under the management of management function unit21. The image can also be input by performing an input processing of anyfile of digital-image files (such as MPEG 2 file and JPEG file group,for example) that are previously accumulated in digital-image filestorage unit 3 and can also be held as a fish-eye image. To see imagesin the desired direction, the user (audience) can use input device 4such as a joystick mouse to input the user-desired sight-line direction(theta phi), zoom magnification (field angle gamma) to the device of theembodiment. The input information is informed via interface 14 tomanagement function unit 21. A simple keyboard mouse input is alsopossible as an input method for the input information.

FIG. 5 is a flowchart of the processing flow of image providing device1.

Management function unit 21 includes a plurality of management modes.These management modes have (1) a mode for inputting real-time imagefrom the fish-eye photographing system, (2) a mode for inputtingaccumulated image from the file, (3) a mode for inputting sight-linedirection and zoom magnification for display and for controllingdisplay.

Management function unit 21 first operates to determine whether thefish-eye image reading is in the real-time type image input mode oraccumulated image input mode (S1). If the reading is in the real-timetype image input mode, the image is read in real-time via inputprocessing unit 11 from fish-eye imaging device 2 (S2). If the readingis in the accumulated image input mode, the digital-image file is readvia input processing unit 11 from digital-image file storage unit 3(S3). After read, the fish-eye image is sequentially stored in fish-eyeimage storage unit 16.

In parallel with this, management function unit 21 performs the mode forinputting sight-line direction and zoom magnification for display andfor controlling display to read from input device 4 the sight-linedirection (theta, phi) and zoom magnification (gamma) as inputinformation (S4). To see images in the desired direction, the user(audience) can use input device 4 such as a joystick mouse to change inreal-time the desired sight-line direction and zoom magnification likethe photographing operation of the camera. Management function unit 21reads the input information in real-time.

After reading the sight-line direction (theta, phi) and zoommagnification (gamma), management function unit 21 computes the valuesof Ku and Kv specifying the extent of the drawing area based on theabove-mentioned Equation 1 (S5). The Ku and Kv are preferably specifiedalso in view of characteristic parameters such as previously stored lenscharacteristics and CMOS (or CCD) characteristics. Dewarping computingmodule 22 performs the dewarping processing for the drawing area (S7).Management function unit 21 uses the dewarped image to draw on outputdevice 5 such as a monitor (S8). The above-described processings areperformed each time the input information is read.

The dewarping processing will now be-described. FIG. 6 schematicallyshows the processing in the dewarping module. Dewarping computing module22 performs the computation processing of the three-dimensional positionof each pixel in the drawing area (S11) and three-dimensional non-lineartexture mapping processing. (S12) to dewarp the fish-eye image to createthe dewarped image.

The computation processing of the three-dimensional position of eachpixel in the drawing area (S11) is conducted by, firstly inputting theextents Ku and Kv of the drawing areas calculated in management functionunit 21, sight-line direction (theta, phi) provided by input device 4,and previously stored characteristic parameters of the lens and theimaging system and the like, and then operating the above-describedEquation 2 to compute the three-dimensional position (Px, Py, Pz) ofeach pixel (Ps) in plane A indicating the drawing area with updated uand v.

Non-linear texture mapping processing (S12) substitutes the computedresults of the three-dimensional position (Px, Py, Pz) of each pixelinto the above-described Equations 3 to 5 to calculate the pixelposition (x_pixel, y_pixel) in the original fish-eye image G thatcorresponds to each pixel position in the dewarped image to be drawn inthe drawing area, and maps the color information (such as RGB and YUV)at the pixel position in the original fish-eye image G to thecorresponding pixel in the drawing area.

As seen in the equations (Equations 1 to 5), the computation processingof the three-dimensional position (S11) and non-linear texture mappingprocessing (S12) can be performed independently for each pixel.Processings for a plurality of pixels can thus be computed in parallel.As shown in FIG. 7, therefore, more hardware resources available such asCPU can provide more parallelism and less computation time in thecomputation processing (S11 and S12). This can draw a high-image-qualityimage in real-time and in an interactive manner.

The Second Embodiment

The processing of dewarping computing module 22 can be performed evenmore quickly using the graphics function such as a graphics dedicatedprocessor (GPU). Specifically, significant processing can be performedon the graphics-board side by considering plane A indicating the drawingarea in FIG. 1 as the object of the texture mapping performed inthree-dimension.

FIG. 8 shows the dewarping processing using the graphics function. Theprocessing falls into application software and graphics processing. Theapplication software calculates the three-dimensional position of eachpoint at four corners in the drawing area (P0, P1, P2, and P3 in FIG. 2)(S21). The three-dimensional texture mapping and indent processing ofthe graphics processing on the graphics-board side performs thecomputation of each pixel position in the drawing area (S22) andnon-linear texture mapping processing (S23). The interpolationprocessing from the three-dimensional positions of the four cornerscomputes each pixel position in the drawing area.

The calculation processing of the three-dimensional position of eachpoint at four corners in the drawing area (S21) determines the directionvector V as shown in FIG. 2 based on the sight-line direction (theta,phi), zoom magnification (field angle gamma), and characteristicparameters which are provided as input information. Axis vector Eu maybe determined since its Z-component is zero and it is orthogonal withthe direction vector V.

The following Equation 6 can compute axis vector Ev.Ev=V×Eu(vector outer product)   (Equation 6)

Because of the zoom magnification (field angle gamma) being defined,plane A to be displayed has an extent within (−tan gamma/2, tan gamma/2)on Eu-axis. Because of the aspect ratio alpha being known from thedrawing window size, the extent is within (−alpha*tan gamma/2, alpha*tangamma/2) on Ev-axis. The three-dimensional coordinate values at fourcorners can thus be determined as follows using vector notation.V+(−tan gamma/2)Eu+(−alpha*tan gamma/2)EvV+(−tan gamma/2)Eu+(alpha*tan gamma/2)EvV+(tan gamma/2)Eu+(−alpha*tan gamma/2)EvV+(tan gamma/2)Eu +(alpha*tan gamma/2)Ev   (Equation 7)

Three-dimensional coordinates (Px, Py, Pz) of each point interpolated isthen computed on the graphics-board side. The inverse function of thetrigonometric function in the above-described Equation 3 used innon-linear texture mapping processing (S23) can be processed even morequickly by approximating the numerator and denominator withfour-dimensional rational polynomials.

The Third Embodiment

When the drawing area is previously established, and the processing islimited to this drawing area, only a portion of the original fish-eyeimage G will be processed. Management function unit 21 in FIG. 4 thuscuts out a portion of the original fish-eye image G for the processing.

Suppose that, for example, fish-eye image G divides into a plurality ofblocks g and the decoding processing occurs for each block, as in FIG.9. In the embodiments of the present invention, it is supposed that Kuand Kv shown in Equation 1 and three-dimensional positions at fourcorners shown in Equation 7 are determined. The embodiment then usessuch information to calculate the coordinate values of eight points P1to P8 around the area to be processed, and incorporates only blocks g(hatched blocks in FIG. 9) containing these coordinate values as theblocks to be processed in input processing unit 11. This is possible inMPEG 2 and JPEG and the like, for example, by specifying the macroblocks to be processed. In CMOS camera, only cells to be processed maybe captured.

Step S6 in FIG. 5 shows this processing. After the values of Ku and Kvare computed (S5), the cut-out blocks in the original fish-eye image arecalculated (S6), and the limited number of images are read for thehigher speed processing.

The Fourth Embodiment

FIG. 10 shows the stereo image display system according to the fourthembodiment of the present invention. This system includes: twofish-eye-lens-equipped cameras 31 and 32 disposed in parallel; computer33 containing two sets of image providing devices for the dewarpingprocessing of the right and left fish-eye images from cameras 31 and 32;input device 34 for inputting the sight-line direction and zoommagnification to computer 33; output device 35 such as a monitor foralternately displaying the right and left dewarped images dewarped bycomputer 33; and liquid crystal shutter glasses 36 operating insynchronization with output device 35. Output device 35 may use anaked-eye stereovision display to omit liquid crystal shutter glasses36.

As shown in FIG. 11, virtual camera planes can be provided to the userwhich planes specify the same sight-line direction and zoommagnification for the two cameras corresponding to the right eye andleft eye, respectively, and the stereoscopic images can be provided evenby changing the virtual camera planes in an interactive manner at thesame time. Specifically, images in the desired direction can be observedstereoscopically in an interactive manner. When the sight-line changesfrom the front, a difference always occurs in the depth between onevirtual camera plane and the other as shown in FIG. 12. One plane canthus be corrected to be parallel with respect to the sight-linedirection to make it possible to observe images stereoscopically.

As described above, the distortion of the fish-eye lens can be dewarpedquickly to help draw moving images quickly at any sight line and zoom.In addition, monitoring and appreciation can be done with interactivestereoscopic images.

Such a system can draw moving images quickly and apply to broadcastingarea available in real-time, image monitoring for in-vehicle use, andthe like. Additionally, use of the system in stereovision can extend theappreciation of contents in the broadcasting area, for example. Formonitoring use, the system can be mounted on a vehicle for lookingaround extensively and stereoscopically in operating the vehicle in anarrow space such as parallel parking, which is very useful.

INDUSTRIAL APPLICABILITY

The present invention is suited for application in real-time distributedcontents such as broadcasting and mobile phone service,recording-and-reproducing type contents such as packaged media, and thelike, particularly, in surveillance for vehicle operation support, andplant monitoring.

Additionally, use of the system in stereovision can extend theappreciation of contents in the broadcasting area, for example. Formonitoring use, the system can be mounted on a vehicle for lookingaround extensively and stereoscopically in operating the vehicle in anarrow space such as parallel parking, which is very useful.

1. An image-providing device comprising: a fish-eye image input deviceinputting fish-eye image; a fish-eye image storage device storing saidinput fish-eye image; a visual-field information input device inputtingin real-time visual-field information including information onsight-line direction (theta, phi) and on field angle (gamma) invisual-field area of said fish-eye image; a drawing area calculationdevice for calculating in real-time, using said input visual-fieldinformation, each pixel of a drawing area in a plane which is orthogonalto said sight-line direction and has an extent determined by said fieldangle; and a dewarping processing device determining a pixel position insaid fish-eye image which corresponds to each pixel position in saidcalculated drawing area to form in real-time a dewarped image from thefish-eye image with its distortion removed.
 2. An image-providing deviceaccording to claim 1, wherein said fish-eye image is a moving image. 3.An image providing device according to claim 1 wherein on an assumptionthat said fish-eye image is an image derived from an object imaged on ahemispherical surface of a virtually established hemisphere beingdeveloped on a plane, said drawing area calculating device calculates aplane tangent to said hemispherical surface as the drawing area, saiddewarping processing device comprises: a three-dimensional positioncomputation device computing, for each pixel in said calculated drawingarea, its three-dimensional position in a three-dimensional coordinatesystem with an origin at a center of a bottom circle of said hemisphere;and a non-linear mapping device calculating a zenithal angle theta s andan azimuthal angle phi s of an axis passing through said origin and athree-dimensional position of each pixel in said calculated drawingarea, and using these zenithal angle and azimuthal angle as a basis todetermine a pixel position in said fish-eye image.
 4. An image providingdevice according to claim 1, wherein said drawing area calculatingdevice calculates pixel positions at four corners of said drawing area,said dewarping processing device calculates each pixel position in saiddrawing area from the pixel positions at the four corners in saiddrawing area by interpolation processing.
 5. An image providing deviceaccording to claim 1, wherein said fish-eye images are divided into aplurality of blocks, each of which is separately accessible, said imageproviding device further comprises to-be-read block calculating devicecalculating said blocks to be read from said calculated drawing area,and said fish-eye image input device only inputs said calculated blockto be read.
 6. An image providing device according to claim 1, whereinsaid fish-eye image includes right and left two-system images for stereodisplay, said drawing area calculating device calculates a drawing areafor each of said two-system fish-eye images based on said inputvisual-field information, and said dewarping processing device forms,for each of said calculated two-system drawing areas, a dewarped imagefrom each fish-eye image.
 7. An image providing method comprising:inputting a fish-eye image and storing it in a storage device; inputtingin real-time visual-field information including information onsight-line direction (theta, phi) and on field angle (gamma) invisual-field area of said fish-eye image; calculating in real-time,using said input visual-field information, each pixel of a drawing areain a plane which is orthogonal to said sight-line direction and has anextent determined by said field angle; and determining a pixel positionin said fish-eye image which corresponds to each pixel position in saidcalculated drawing area to form in real-time a dewarped image from thefish-eye image with its distortion removed.
 8. An image providing methodaccording to claim 7, wherein said fish-eye image is a moving image. 9.An image providing method according to claim 7, wherein on an assumptionthat said fish-eye image is an image derived from an object imaged on ahemispherical surface of a virtually established hemisphere beingdeveloped on a plane, said step of calculating a drawing area inreal-time calculates a plane tangent to said hemispherical surface asthe drawing area, and said step of forming a dewarped image in real-timecomprises: computing, for each pixel in said calculated drawing area,its three-dimensional position in a three-dimensional coordinate systemwith an origin at a center of a bottom circle of said hemisphere; andcalculating a zenithal angle theta s and an azimuthal angle phi s of anaxis passing through said origin and a three-dimensional position ofeach pixel in said calculated drawing area, and using these zenithalangle and azimuthal angle as a basis to determine a pixel position insaid fish-eye image.
 10. An image providing method according to claim 7,wherein said step of calculating a drawing area in real-time calculatespixel positions at four corners of said drawing area, and said step offorming a dewarped image in real-time calculates each pixel position insaid drawing area from the pixel positions at the four corners in saiddrawing area by interpolation processing.
 11. An image providing methodaccording to claim 7, further comprising: dividing said fish-eye imagesinto a plurality of blocks, each of which is separately accessible; andcalculating said blocks to be read from said calculated drawing area.12. An image providing method according to claim 7, wherein saidfish-eye image includes right and left two-system images for stereodisplay, said step of calculating a drawing area in real-time calculatesa drawing area for each of said two-system fish-eye images based on saidinput visual-field information, and said step of forming a dewarpedimage in real-time forms, for each of said calculated two-system drawingareas, a dewarped image from each fish-eye image.